Numerical calculations are performed for the problem of penetration into a vortex core of a blade travelling normal to the vortex axis, where the plane formed by the blade span and the direction of blade motion coincides with the normal plane of the vortex axis at the point of penetration. The calculations are based on a computational method, applicable for unsteady three-dimensional flow past immersed bodies, in which a collocation solution of the vorticity transport equation is obtained on a set of Lagrangian control points. Differences between this method and other Lagrangian vorticity-based methods in the literature are discussed. Lagrangian methods of this type are particularly attractive for problems of unsteady vortex-body interaction, since control points need only be placed on the surface of the body and in regions of the flow with non-negligible vorticity magnitude. The computations for normal blade-vortex interaction (BVI) are performed for an inviscid fluid and focus on the relationship between the vortex core deformation due to penetration of the blade into the vortex ambient position and the resulting unsteady pressure field and unsteady force acting on the blade. Computations for cases with different vortex circulations are performed, and the accuracy of an approximate formulation using rapid distortion theory is assessed by comparison with the full computational results for unsteady blade force. The force generated from blade penetration into the vortex ambient position is found to be of a comparable magnitude to various other types of unsteady BVI forces, such as that due to cutting of the vortex axial flow.

A computational study of the penetration of a blade into the core of an initially columnar vortex in an incompressible viscous fluid and the subsequent cutting of the vortex is reported for the case where the blade axis is initially orthogonal to the vortex axis. The vortex is advected toward the fixed blade by a free-stream velocity oriented tangent to the blade chord, where the free-stream speed is sufficiently large that the vortex does not induce ejection of vorticity from the blade boundary layer prior to impact of the vortex core with the blade leading edge. A range of computations are performed for cases both with and without ambient axial flow in the vortex core. As the blade leading edge penetrates into the vortex core, cross-diffusion between the columnar vortex and the blade boundary layer causes vortex lines originating in the columnar vortex to rapidly reconnect to those in the blade boundary layer. This cutting process is found to be always incomplete however, due to a change in sign of the spanwise vortex-induced velocity along the leading edge as the vortex is cut, leaving a thin vortex sheet that wraps around the blade leading edge. Cutting of a vortex with non-zero axial flow causes an asymmetry that results in an impulsive lift force on the blade. This lift force has maximum magnitude during the time period where the blade leading edge penetrates into the vortex core. Both the vortex cutting process and the unsteady lift force on the blade are found to be approximately independent of Reynolds number for the various cases examined.

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The aerodynamic operating environment of the helicopter is particularly complex and, to some extent, dominated by the vortices trailed from the main and tail rotors. These vortices not only determine the form of the induced flow field but also interact with each other and with elements of the physical structure of the flight vehicle. Such interactions can have implications in terms of structural vibration, noise generation and flight performance. In this paper, the interaction of main rotor vortices with the helicopter tail rotor is considered and, in particular, the limiting case of the orthogonal interaction. The significance of the topic is introduced by highlighting the operational issues for helicopters arising from tail rotor interactions. The basic phenomenon is then described before experimental studies of the interaction are presented. Progress in numerical modelling is then considered and, finally, the prospects for future research in the area are discussed.

A study is reported of the wind-driven breakoff of rivulets and subsequent droplet flows on a horizontal plate subject to different normal gravitational states, ranging from zero- to terrestrial-gravity conditions (1 g), and including some data for partial gravity conditions (between 0.1 g and 0.38 g). The study entailed experiments conducted in the authors’ laboratory at the University of Iowa and onboard the NASA KC-135, parabolic-flight aircraft. The wind-driven rivulets exhibited a breakoff phenomenon over a broad range of flow rates, in which a “head” at the tip of the rivulet broke off periodically to form a droplet that advected down the plate. The rivulet breakoff phenomena was sensitive to the normal gravitational force acting on the plate. For instance, the frequency of rivulet breakoff was nearly an order-of-magnitude greater for the 0 g condition than for the same flow in the 1 g condition. The droplet shape and behavior were observed to be quite different between the two cases. It was furthermore found in all cases examined that wind-driven rivulet and droplet flows are markedly different from gravitationally driven flows. These differences arise primarily from the role of form drag on the droplets and on the raised ridge of the rivulet and pool flows near the moving contact line.

A study was performed using direct numerical simulation to examine the interaction of external turbulence with a nominally columnar, large-scale vortex at a vortex Reynolds number $\hbox{\it Re}_V \,{\equiv}\, \Gamma / \nu \,{=}\, 3000$. A multi-step procedure is used to generate initial conditions in which the external turbulence has the wrapped, nearly azimuthal form characteristic of turbulence around a large-scale vortex structure. The proper-orthogonal decomposition method is used to extract specific modes of the vortex turbulence that dominate the kinetic energy and enstrophy fields. The effect of turbulence initial intensity and length scale on the turbulence structure and its influence on the large-scale vortex are examined. It is observed that the external turbulence wraps around the large-scale vortex and advects radially inward toward the vortex core. The dominant axial length scale of the external turbulence appears to scale with the vortex core diameter, with the mode with the largest enstrophy having a wavelength of about twice the core diameter. The turbulence induces a bending wave on the vortex core with axial wavelength approximately equal to the dominant wavelength of the external turbulence. The turbulent enstrophy decays according to a power-law expression for cases with moderate initial turbulence intensity. For sufficiently strong initial turbulence intensity, the turbulence breaks up the large-scale vortex core, creating strong turbulence within the vortex core.

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